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Unformatted text preview: UCSB Spring 2011 ECE 146B: Communications II Lab 4: Introduction to OFDM Assigned: May 10 Due: May 30 (by noon in the course homework box)) Reading: Chapters 4 and 6; background section in this lab assignment Lab Objectives: To learn about Orthogonal Frequency Division Multiplexing (OFDM) for communi cation over dispersive channels. Background We have seen in Chapter 4 that, for an ideal channel, intersymbol interference (ISI) can be avoided in linearly modulated systems by designing the transmit and receive filters so that their cascade is Nyquist at the desired symbol rate; that is, symbols can be isolated from each other, provided that we sample at the appropriate times. However, since we typically do not have control over the channel, a Nyquist design still incurs ISI when the channel is dispersive. Lab 3 provided a handson introduction to equalization techniques for compensating such ISI. In this lab, we introduce an alternative approach to communication over dispersive channels whose goal is to isolate symbols from each other for any dispersive channel. The idea is to employ frequency domain transmission, sending symbols B [ n ] using complex exponentials s n ( t ) = e j 2 πf n t , which have two key properties: P1) When s n ( t ) goes through an LTI system with impulse response h ( t ) and transfer function H ( f ), the output is a scalar multiple of s n ( t ). Specifically, e j 2 πf n t ∗ h ( t ) = H ( f n ) e j 2 πf n t P2) Complex exponentials at different frequencies are orthogonal: ( s n ,s m ) = integraldisplay s n ( t ) s ∗ m ( t ) dt = integraldisplay ∞ −∞ e j 2 π ( f n − f m ) t dt = δ ( f m − f n ) = 0 , f n negationslash = f m This is analogous to the properties of eigenvectors of matrices. Thus, complex exponentials are eigen functions of any LTI system. Conceptual basis for OFDM: For frequency domain transmission with symbol B [ k ] modulating the complex exponential s n ( t ) = e j 2 πf n t , the transmitted signal is given by u ( t ) = summationdisplay n B [ n ] e j 2 πf n t When this goes through a dispersive channel h ( t ), we obtain (ignoring noise) ( u ∗ h )( t ) = summationdisplay n B [ n ] H ( f n ) e j 2 πf n t Note that the symbols { B [ n ] } do not interfere with each other after passing through the channels, since different complex exponentials are orthogonal. Furthermore, regardless of how complicated the time domain channel h ( t ) is, in the frequency domain, the problem of equalization has been parallelized: we only need to estimate and compensate for the complex scalar H ( f n ) in demodulating the n th symbol. We now discuss how to translate this concept into practice. Finite signaling interval: The first step is to constrain the signaling interval, say to length T . The complex baseband transmitted signal is therefore given by u ( t ) = N − 1 summationdisplay n =0 B [ n ] e j 2 πf n t I [0 ,T ] ( t ) = N − 1 summationdisplay n =0 B [ n ] p n ( t ) (1) where B [ n ] is the symbol transmitted using the modulating signal...
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This note was uploaded on 09/10/2011 for the course ECE 146B taught by Professor Upamanyumadhow during the Spring '11 term at UC Merced.
 Spring '11
 UpamanyuMadhow

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